Question

A piece of wood has a mass of 20 grams and a volume of \(25 \mathrm{~cm}^3\). What is the density of the wood in grams per \(\mathrm{cm}^3\) ? A. \(0.8 \mathrm{~g} / \mathrm{cm}^3\) B. \(0.9 \mathrm{~g} / \mathrm{cm}^3\) C. \(1.2 \mathrm{~g} / \mathrm{cm}^3\) D. \(1.3 \mathrm{~g} / \mathrm{cm}^3\)

Short answer

The density of the wood is 0.8 g/cm^3. Answer: A.

Step-by-step solution

Know the formula for density

Density (\text{density}) is defined as mass (\text{mass}) divided by volume (\text{volume}). The formula is: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Identify the given values

The problem states that the mass (\text{mass}) of the wood is 20 grams and the volume (\text{volume}) is 25 \( \mathrm{cm}^3 \).

Substitute the values into the formula

Replace \text{mass} with 20 and \text{volume} with 25 in the formula from Step 1: \[ \text{Density} = \frac{20 \text{ g}}{25 \text{ } \mathrm{cm}^3} \]

Calculate the density

Divide 20 grams by 25 \( \mathrm{cm}^3 \): \[ \text{Density} = \frac{20}{25} = 0.8 \text{ g/} \mathrm{cm}^3 \]

Verify the answer

Check the calculated density against the provided options. The correct choice is: A. \(0.8 \mathrm{~g} / \mathrm{cm}^3\)

Key concepts

Mass

Mass refers to the amount of matter in an object. It is a fundamental property that doesn't change regardless of the object's location. For example, a piece of wood has a mass of 20 grams whether it's on Earth or the Moon.

Mass is measured in units such as grams (g), kilograms (kg), and milligrams (mg). Understanding mass is crucial because it is one of the primary variables used in the density formula.

Volume

Volume is the amount of space an object occupies. In our exercise, the volume of the wood is 25 \( \mathrm{cm}^3 \).

Common units for measuring volume include cubic centimeters (\( \mathrm{cm}^3 \)), liters (L), and milliliters (mL). To easily visualize volume, consider a small cube that measures 1 cm on each side—its volume would be 1 \( \mathrm{cm}^3 \). Volumes can be calculated for regular shapes using mathematical formulas or measured for irregular shapes using displacement methods.

Density Formula

Density is a measure of how much mass is contained in a given volume. The formula for density is: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

For the piece of wood, we know the mass is 20 grams and the volume is 25 \( \mathrm{cm}^3 \). By substituting these values into the density formula, we calculate the density as: \[ \text{Density} = \frac{20 \text{ g}}{25 \text{ } \mathrm{cm}^3} = 0.8 \text{ g/cm}^3 \]

This tells us that each cubic centimeter of the wood contains 0.8 grams of mass.

Unit Conversion

Sometimes, you'll need to convert units to make calculations easier. For density calculations, it's essential to have mass and volume in compatible units, such as grams and cubic centimeters.

Common conversions include:

• 1 kilogram (kg) = 1000 grams (g)
• 1 liter (L) = 1000 milliliters (mL) = 1000 cubic centimeters (\( \mathrm{cm}^3 \))

Keeping track of units ensures accurate calculations and helps avoid errors in your density computations.